Lagrangian formalism of gravity in the Randall-Sundrum model

Abstract

We derive the effective Lagrangian of the physical four-dimensional fields in the Randall-Sundrum (RS) model, and use this to calculate the Newtonian gravitational potential between two point sources on the brane. The effect of the radion is emphasized, and it is shown to disappear when the hidden brane is taken to infinity, i.e. when we only have one brane. As a preliminary, we derive the corresponding Lagrangian in the simpler geometry of a flat spacetime with one extra dimension compactified on a torus. We also study the gauge invariance of the theory, and note that the massless vector field that is present for the torus disappears in the RS model because of the orbifold symmetry.

10 pages, latex with revtex4, 5 postscript figures; Section on gauge transformations added, conclusions unchanged

References in corpus (3)

• Higher order corrections to the Newtonian potential in the Randall-Sundrum model
• Two-Brane Randall-Sundrum Model in AdS_5 and dS_5
• Gravitational Forces in the Brane World

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